Would an artificial general intelligence have to be Turing complete?
My answer is yes, but in a trivial way. The least you would expect from an intelligent agent is that it is able to execute a given Turing machine on a given input. This requires actually no intelligence, just following rules. If however, you are referring to the capability of predicting if the Turing machine will terminate on the given input, that is another matter. I don't think it is reasonable to expect such "undecidable" computational power for an agent to be generally intelligent.